More than fifty years ago Ronald Coase published ‘The Problem of Social Cost’. In his paper, Professor Coase presents an intriguing idea that has since become known among economists and lawyers as the ‘Coase Theorem’. Unlike most modern forms of economic analysis, however, Coase’s Theorem is based on a verbal argument and is almost always proved arithmetically. That is to say, the Coase Theorem is not really a theorem in the formal or mathematical sense of the word. Our objective in this paper, then, is to remedy this deficiency by formalizing the logic of the Coase Theorem. In summary, we combine Coase’s intuitive insights with the formal methods of game theory.